When we limit RT analysis to strong left and right handers with EHI scores of +-100, the critical three-way interaction effect is stronger (23.51ms, 95% CI [7.10, 39.92], p = .0025, one-sided), and left handers’ LVF global bias is closer to zero (4.59ms (95% CI [-7.80, 16.98]; the effect for right handers is 28.10ms, 95% CI [17.34, 38.86]). We still see a null result for accuracy, but the point estimates are now in the predicted direction (OR = 1.10, 95% CI [0.75, 1.61], p = .32, one-sided; where OR < 1 means greater LVF global bias for left handers).
Demographics for included participants, by handedness group (EHI bins).
| Handedness | N | Age (years) | Education (years) | Sex (M/F/O) | EHI |
|---|---|---|---|---|---|
| Left | 138 | 30.07 (5.87) | 14.68 (2.45) | 81/56/1 | -100 (0) |
| Mixed | 524 | 28.55 (5.99) | 14.31 (2.48) | 264/250/10 | -0.19 (63.85) |
| Right | 182 | 29.87 (6.14) | 14.34 (2.48) | 96/85/1 | 100 (0) |
| Left: (EHI = -100) | Right: (EHI = +100) | Mixed: Everyone in between | |||||
Do we find an interaction of field x level x handedness, when
handedness is binned as left (EHI = -100) or right (EHI = +100)?
Summary. For reaction time, we find the critical interaction in the predicted direction (23.51ms, 95% CI [7.10, 39.92], p = .0025, one-sided). Left handers show 4.59ms LVF global bias (95% CI [-7.80, 16.98]), and right handers 28.10ms (95% CI [17.34, 38.86]). Mixed handers (not included in the categorical interaction analysis) show a LVF global bias of 24.195ms (95% CI [17.82, 30.58]).
For accuracy, we find no significant interaction of field by level by handedness (OR = 1.10, 95% CI [0.75, 1.61], p = .32, one-sided; where OR < 1 means greater LVF global bias for left handers). Point estimates of LVF global bias hardly differ between left handers (OR = 1.67, 95% CI [1.26, 2.22]) and right handers (OR = 1.84, 95% CI [1.42, 2.38]). For mixed handers (not included in the categorical interaction analysis), the point estimate is 1.67 (95% CI [1.44, 1.93]).
Error bars show 95% CI. Left handers are those with EHI = -100; Right handers, EHI = +100. “Mixed handers” are everyone with EHI values in between -100 and +100.
Reaction time is modeled as a linear effect of field, level, and
handedness, using data from every target-present trial with a “go”
response:
lmer( rt ~ field*level*handedness + (1 | subject) )
| Field by level by handedness interaction (RT) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 9 | 526,319.708 | 526,396.837 | −263,150.854 | 526,301.708 | - | - | - |
| 10 | 526,313.82 | 526,399.519 | −263,146.91 | 526,293.82 | 7.888 | 1 | .005 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level by handedness interaction (RT) | |||||||||
| Compare effect estimate to zero with emmeans() | |||||||||
| field_consec | level_consec | handedness_consec | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Right - Left | 23.514 | 8.373 | Inf | 7.104 | 39.924 | 2.808 | .005 |
| 1 A positive number means LVF global bias is stronger in right handers (as predicted by AAH) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Two-sided | |||||||||
| LVF Global bias by handedness bin (RT) | |||||||||
| field_consec | level_consec | handedness | estimate1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Left | 4.587 | 6.322 | Inf | −7.804 | 16.979 | 0.726 | .468 |
| LVF - RVF | Local - Global | Right | 28.101 | 5.489 | Inf | 17.343 | 38.86 | 5.119 | <.0001 |
| 1 A positive number means global bias (faster RT for global) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Two-sided, uncorrected | |||||||||
| LVF Global bias by handedness bin, including mixed (RT) | |||||||||
| field_consec | level_consec | handedness | estimate1 | SE | df2 | asymp.LCL3,4 | asymp.UCL3,4 | z.ratio | p.value5 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Left | 4.587 | 6.349 | Inf | −7.856 | 17.03 | 0.723 | .47 |
| LVF - RVF | Local - Global | Mixed | 24.195 | 3.255 | Inf | 17.815 | 30.575 | 7.433 | <.0001 |
| LVF - RVF | Local - Global | Right | 28.101 | 5.512 | Inf | 17.298 | 38.904 | 5.098 | <.0001 |
| 1 A positive number means global bias (faster RT for global) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Left: EHI = -100; Right: EHI = +100; Mixed: Everyone else. These mixed handers were not included in the model. | |||||||||
| 5 Two-sided, uncorrected | |||||||||
| LVF Global bias by handedness bin, including mixed (RT) | |||||||||
| field_consec | level_consec | handedness | estimate1 | SE | df2 | asymp.LCL3,4 | asymp.UCL3,4 | z.ratio | p.value5 |
|---|---|---|---|---|---|---|---|---|---|
| LVF - RVF | Local - Global | Strong Left | 4.587 | 6.348 | Inf | −7.855 | 17.03 | 0.723 | .47 |
| LVF - RVF | Local - Global | Weak Left | 24.329 | 4.389 | Inf | 15.728 | 32.93 | 5.544 | <.0001 |
| LVF - RVF | Local - Global | Weak Right | 23.976 | 4.853 | Inf | 14.463 | 33.489 | 4.94 | <.0001 |
| LVF - RVF | Local - Global | Strong Right | 28.101 | 5.512 | Inf | 17.298 | 38.904 | 5.098 | <.0001 |
| 1 A positive number means global bias (faster RT for global) | |||||||||
| 2 Z-approximation | |||||||||
| 3 Confidence level: 95% | |||||||||
| 4 Strong left: EHI = -100; Weak left: -100 < EHI <= 0; Weak right: 0 < EHI < +100; Strong right: EHI = +100. These mixed handers were not included in the model. | |||||||||
| 5 Two-sided, uncorrected | |||||||||
| Global bias by field, by handedness bin (RT) | |||||||
| level_consec | field | handedness | estimate1 | SE | df2 | z.ratio | p.value3 |
|---|---|---|---|---|---|---|---|
| Local - Global | RVF | Left | 19.678 | 4.479 | Inf | 4.393 | <.0001 |
| Local - Global | LVF | Left | 24.265 | 4.468 | Inf | 5.43 | <.0001 |
| Local - Global | RVF | Right | 5.732 | 3.89 | Inf | 1.473 | .141 |
| Local - Global | LVF | Right | 33.834 | 3.875 | Inf | 8.731 | <.0001 |
| 1 A positive number means global bias (faster RT for global) | |||||||
| 2 Z-approximation | |||||||
| 3 Two-sided, uncorrected | |||||||
| RT (ms) by field, level and handedness bin | |||||||
| field | level | handedness | emmean | SE | df1 | asymp.LCL2 | asymp.UCL2 |
|---|---|---|---|---|---|---|---|
| RVF | Global | Left | 662.211 | 14.833 | Inf | 633.139 | 691.283 |
| LVF | Global | Left | 639.53 | 14.828 | Inf | 610.468 | 668.592 |
| RVF | Local | Left | 681.889 | 14.842 | Inf | 652.799 | 710.979 |
| LVF | Local | Left | 663.795 | 14.844 | Inf | 634.702 | 692.889 |
| RVF | Global | Right | 701.166 | 12.916 | Inf | 675.851 | 726.48 |
| LVF | Global | Right | 686.623 | 12.91 | Inf | 661.319 | 711.927 |
| RVF | Local | Right | 706.898 | 12.921 | Inf | 681.573 | 732.223 |
| LVF | Local | Right | 720.457 | 12.922 | Inf | 695.13 | 745.783 |
| 1 Z-approximation | |||||||
| 2 Confidence level: 95% | |||||||
| Field by level interaction (RT) | |||||
| Old-school Omnibus F-test | |||||
| term | df | sumsq | meansq | statistic | p.value |
|---|---|---|---|---|---|
| field | 1 | 792,986.103 | 792,986.103 | 11.227 | .0008 |
| level | 1 | 4,085,669.668 | 4,085,669.668 | 57.843 | <.0001 |
| handedness | 1 | 16,819,585.24 | 16,819,585.24 | 238.126 | <.0001 |
| field:level | 1 | 749,826.902 | 749,826.902 | 10.616 | .001 |
| field:handedness | 1 | 975,533.562 | 975,533.562 | 13.811 | .0002 |
| level:handedness | 1 | 7,079.075 | 7,079.075 | 0.1 | .752 |
| field:level:handedness | 1 | 318,410.828 | 318,410.828 | 4.508 | .034 |
| Residuals | 38,935 | 2,750,103,740.474 | 70,633.203 | - | - |
summary(rt_model_2bins)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field * level * handedness + (1 | subject)
## Data: aah_for_rt_model_2bins
##
## REML criterion at convergence: 526252.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.899514 -0.587954 -0.155036 0.379780 7.706435
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 28996.0 170.282
## Residual 41783.5 204.410
## Number of obs: 38943, groups: subject, 320
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 662.21065 14.83289 44.64475
## fieldLVF -22.68059 4.43112 -5.11847
## levelLocal 19.67803 4.47932 4.39308
## handednessRight 38.95491 19.66808 1.98062
## fieldLVF:levelLocal 4.58721 6.32234 0.72556
## fieldLVF:handednessRight 8.13809 5.87303 1.38567
## levelLocal:handednessRight -13.94567 5.93288 -2.35057
## fieldLVF:levelLocal:handednessRight 23.51411 8.37274 2.80841
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlLcl hnddnR flLVF:L fLVF:R lvlL:R
## fieldLVF -0.151
## levelLocal -0.149 0.498
## hnddnssRght -0.754 0.114 0.112
## fldLVF:lvlL 0.105 -0.701 -0.707 -0.080
## fldLVF:hndR 0.114 -0.754 -0.376 -0.151 0.529
## lvlLcl:hndR 0.112 -0.376 -0.755 -0.149 0.534 0.499
## fldLVF:lL:R -0.080 0.529 0.534 0.106 -0.755 -0.701 -0.708
Error bars show 95% CI. Left handers are those with EHI = -100; Right handers, EHI = +100. “Mixed handers” are everyone with EHI values in between -100 and +100.
Accuracy is modeled as a binomial effect of field, level, and
handedness, using binary correct/incorrect data from every
target-present trial:
glmer( correct ~ field*level*handedness + (1 | subject), family = "binomial" )
| Field by level by handedness interaction (Accuracy) | |||||||
| ANOVA: compare models with vs. without interaction term | |||||||
| npar | AIC | BIC | logLik | deviance | Chisq | Df | p.value1 |
|---|---|---|---|---|---|---|---|
| 8 | 14,746.416 | 14,815.379 | −7,365.208 | 14,730.416 | - | - | - |
| 9 | 14,748.19 | 14,825.773 | −7,365.095 | 14,730.19 | 0.226 | 1 | .634 |
| 1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html) | |||||||
| Field by level by handedness interaction (Accuracy) | ||||||||||
| Compare effect estimate to zero with emmeans() | ||||||||||
| field_consec | level_consec | handedness_consec | odds.ratio1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | null | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|---|
| LVF / RVF | Global / Local | Right / Left | 1.1 | 0.215 | Inf | 0.751 | 1.613 | 1 | 0.489 | .625 |
| 1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF for right handers (predicted by AAH) | ||||||||||
| 2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp. | ||||||||||
| 3 Confidence level: 95% | ||||||||||
| 4 Two-sided | ||||||||||
| LVF Global bias by handedness bin (Accuracy) | ||||||||||
| Compare effect estimate to zero with emmeans() | ||||||||||
| field_consec | level_consec | handedness | odds.ratio1 | SE | df2 | asymp.LCL3 | asymp.UCL3 | null | z.ratio | p.value4 |
|---|---|---|---|---|---|---|---|---|---|---|
| LVF / RVF | Global / Local | Left | 1.671 | 0.242 | Inf | 1.258 | 2.22 | 1 | 3.546 | .0004 |
| LVF / RVF | Global / Local | Mixed | 1.668 | 0.124 | Inf | 1.442 | 1.93 | 1 | 6.876 | <.0001 |
| LVF / RVF | Global / Local | Right | 1.842 | 0.242 | Inf | 1.423 | 2.384 | 1 | 4.64 | <.0001 |
| 1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF, as predicted for right handers. Mixed handers' global bias is shown here, but their data was not included in the binomial model. | ||||||||||
| 2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp. | ||||||||||
| 3 Confidence level: 95% | ||||||||||
| 4 Two-sided | ||||||||||
summary(acc_model_2bins)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
## Data: aah_for_acc_model_2bins
##
## AIC BIC logLik deviance df.resid
## 14748.2 14825.8 -7365.1 14730.2 40951
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.749323 0.116289 0.168889 0.247757 0.836170
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.02035 1.01012
## Number of obs: 40960, groups: subject, 320
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.0553598 0.1098501 27.81390
## fieldLVF -0.0683805 0.0854800 -0.79996
## levelGlobal 0.4950481 0.0964275 5.13389
## handednessRight 0.1251428 0.1452307 0.86168
## fieldLVF:levelGlobal 0.5130782 0.1447220 3.54527
## fieldLVF:handednessRight 0.0264166 0.1159943 0.22774
## levelGlobal:handednessRight -0.1367240 0.1288284 -1.06129
## fieldLVF:levelGlobal:handednessRight 0.0954962 0.1951619 0.48932
## Pr(>|z|)
## (Intercept) < 2.22e-16 ***
## fieldLVF 0.42373447
## levelGlobal 0.00000028382 ***
## handednessRight 0.38886230
## fieldLVF:levelGlobal 0.00039221 ***
## fieldLVF:handednessRight 0.81984824
## levelGlobal:handednessRight 0.28855899
## fieldLVF:levelGlobal:handednessRight 0.62461684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF -0.400
## levelGlobal -0.348 0.453
## hnddnssRght -0.740 0.302 0.264
## fldLVF:lvlG 0.237 -0.589 -0.664 -0.179
## fldLVF:hndR 0.294 -0.736 -0.333 -0.408 0.433
## lvlGlbl:hnR 0.261 -0.338 -0.747 -0.363 0.496 0.458
## fldLVF:lG:R -0.175 0.436 0.491 0.243 -0.740 -0.592 -0.658